Simon Benninga. Financial Modelling 3-rd edition
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x Contents
7.5 Accounting for Leveraged Leases: The “Multiple Phases
Method” 230
7.6 Comparing the MPM Rate of Return with the IRR 234
7.7 Summary 234
Exercises 235
II Portfolio Models 237
8 Portfolio Models—Introduction 239
8.1 Overview 239
8.2 Computing Returns for Walmart and Target 239
8.3 Calculating Portfolio Means and Variances 245
8.4 Portfolio Means and Variances—The General Case 246
8.5 Effi cient Portfolios 250
8.6 Conclusion 252
Exercises 252
Appendix 1: Adjusting for Dividends 255
Appendix 2: Continuously Compounded versus Geometric
Returns 257
9 Calculating Effi cient Portfolios When There Are No
Short-Sale Restrictions 261
9.1 Overview 261
9.2 Some Preliminary Defi nitions and Notation 261
9.3 Some Theorems on Effi cient Portfolios and CAPM 263
9.4 Calculating the Effi cient Frontier: An Example 268
9.5 Three Notes on the Optimization Procedure 272
9.6 Finding Effi cient Portfolios in One Step 276
9.7 Finding the Market Portfolio: The Capital Market Line 278
9.8 Testing the SML: Implementing Propositions 3–5 280
9.9 Summary 283
Exercises 283
Appendix 285
10 Calculating the Variance-Covariance Matrix 291
10.1 Overview 291
10.2 Computing the Sample Variance-Covariance Matrix 291
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10.3 Should We Divide by M or by M – 1? Excel versus
Statistics 295
10.4 Alternate Methods for Computing the Sample Variance-
Covariance Matrix 297
10.5 Computing the Global Minimum Variance Portfolio 299
10.6 Computing an Effi cient Portfolio 301
10.7 Alternatives to the Sample Variance-Covariance: The
Single-Index Model 304
10.8 Alternatives to the Sample Variance-Covariance:
Constant Correlation 306
10.9 Shrinkage Methods 308
10.10 Alternatives to the Variance-Covariance Matrix: Impact
on the Minimum-Variance Portfolio and the Optimal
Portfolio 310
10.11 Summary 315
Exercises 315
11 Estimating Betas and the Security Market Line 317
11.1 Overview 317
11.2 Testing the Security Market Line 320
11.3 Did We Learn Something? 324
11.4 The Ineffi ciency of the “Market Portfolio” 326
11.5 So What’s the Real Market Portfolio? How Can We Test
the CAPM? 329
11.6 Using Excess Returns 330
11.7 Does the CAPM Have Any Uses? 332
Exercises 333
12 Effi cient Portfolios without Short Sales 335
12.1 Overview 335
12.2 A Numerical Example 336
12.3 The Effi cient Frontier with Short-Sale Restrictions 341
12.4 A VBA Program to Create the Effi cient Frontier 343
12.5 Other Position Restrictions 345
12.6 Conclusion 347
Exercises 347
xii Contents
13 The Black-Litterman Approach to Portfolio Optimization 349
13.1 Overview 349
13.2 A Naive Problem 351
13.3 Black and Litterman’s Solution to the Optimization
Problem 357
13.4 Black-Litterman Step 1: What Does the Market Think? 357
13.5 Black-Litterman Step 2: Introducing Opinions—What
Does Joanna Think? 360
13.6 Implementing Black-Litterman on an International
Portfolio 365
13.7 Summary 368
Exercises 369
14 Event Studies 371
14.1 Overview 371
14.2 Outline of an Event Study 371
14.3 An Initial Event Study: Procter & Gamble Buys
Gillette 375
14.4 A Fuller Event Study: Impact of Earnings
Announcements on Stock Prices 382
14.5 Using a Two-Factor Model of Returns for an Event
Study 390
14.6 Using Excel’s Offset Function to Locate a Regression in
a Data Set 394
14.7 Conclusion 396
15 Value at Risk 397
15.1 Overview 397
15.2 A Really Simple Example 397
15.3 Defi ning Quantiles in Excel 399
15.4 A Three-Asset Problem: The Importance of the
Variance-Covariance Matrix 402
15.5 Simulating Data—Bootstrapping 404
Appendix: How to Bootstrap: Making a Bingo Card in
Excel 409
xiii Contents
III Option-Pricing Models 419
16 An Introduction to Options 421
16.1 Overview 421
16.2 Basic Option Defi nitions and Terminology 421
16.3 Some Examples 424
16.4 Option Payoff and Profi t Patterns 426
16.5 Option Strategies: Payoffs from Portfolios of Options
and Stocks 430
16.6 Option Arbitrage Propositions 432
16.7 Summary 439
Exercises 439
17 The Binomial Option-Pricing Model 443
17.1 Overview 443
17.2 Two-Date Binomial Pricing 443
17.3 State Prices 445
17.4 The Multiperiod Binomial Model 449
17.5 Pricing American Options Using the Binomial Pricing
Model 455
17.6 Programming the Binomial Option-Pricing Model in
VBA 458
17.7 Convergence of Binomial Pricing in the Black-Scholes
Price 463
17.8 Using the Binomial Model to Price Employee Stock
Options 466
17.9 Using the Binomial Model to Price Nonstandard
Options: An Example 476
17.10 Summary 478
Exercises 478
18 The Lognormal Distribution 483
18.1 Overview 483
18.2 What Do Stock Prices Look Like? 484
18.3 Lognormal Price Distributions and Geometric
Diffusions 492
18.4 What Does the Lognormal Distribution Look Like? 495
18.5 Simulating Lognormal Price Paths 498
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18.6 Technical Analysis 502
18.7 Calculating the Parameters of the Lognormal
Distribution from Stock Prices 503
18.8 Summary 505
Exercises 505
19 The Black-Scholes Model 509
19.1 Overview 509
19.2 The Black-Scholes Model 509
19.3 Using VBA to Defi ne a Black-Scholes Pricing Function 511
19.4 Calculating the Implied Volatility 513
19.5 A VBA Function to Find the Implied Variance 517
19.6 Dividend Adjustments to the Black-Scholes 520
19.7 Using the Black-Scholes Formula to Price Structured
Securities 525
19.8 Bang for the Buck with Options 539
19.9 The Black (1976) Model for Bond Option Valuation 541
19.10 Summary 544
Exercises 544
20 Option Greeks 549
20.1 Overview 549
20.2 Defi ning and Computing the Greeks 550
20.3 Delta Hedging a Call 555
20.4 Hedging a Collar 564
20.5 Summary 574
Exercises 575
21 Portfolio Insurance 577
21.1 Overview 577
21.2 Portfolio Insurance on More Complicated Assets 578
21.3 An Example 580
21.4 Some Properties of Portfolio Insurance 584
21.5 What Do Portfolio Insurance Strategies Look Like?
A Simulation 585
21.6 Insuring Total Portfolio Returns 588
21.7 Implicit Puts and Asset Values 592
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21.8 Summary 593
Exercises 594
22 An Introduction of Monte Carlo Methods 597
22.1 Overview 597
22.2 Computing π Using Monte Carlo 597
22.3 Writing a VBA Program 602
22.4 Another Monte Carlo Problem: Investment and
Retirement 604
22.5 A Monte Carlo Simulation of the Investment Problem 607
22.6 Summary 610
Exercises 610
23 Using Monte Carlo Methods for Option Pricing 613
23.1 Overview 613
23.2 State Prices, Probabilities, and Risk Neutrality 613
23.3 Pricing a Plain-Vanilla Call Using Monte Carlo
Methods 615
23.4 Monte Carlo Plain-Vanilla Call Pricing Converges to
Black-Scholes 618
23.5 Pricing Asian Options 625
23.6 Pricing Asian Options with a VBA Program 633
23.7 Pricing Barrier Options with Monte Carlo 638
23.8 Using VBA and Monte Carlo to Price a Barrier
Option 642
23.9 Summary 646
Exercises 646
24 Real Options 649
24.1 Overview 649
24.2 A Simple Example of the Option to Expand 650
24.3 The Abandonment Option 653
24.4 Valuing the Abandonment Option as a Series of Puts 659
24.5 Valuing a Biotechnology Project 662
24.6 Conclusion 667
Exercises 667
xvi Contents
IV Bonds 669
25 Duration 671
25.1 Overview 671
25.2 Two Examples 671
25.3 What Does Duration Mean? 674
25.4 Duration Patterns 678
25.5 The Duration of a Bond with Uneven Payments 679
25.6 Nonfl at Term Structures and Duration 687
25.7 Summary 689
Exercises 689
26 Immunization Strategies 693
26.1 Overview 693
26.2 A Basic Simple Immunization Model 693
26.3 A Numerical Example 695
26.4 Convexity: A Continuation of Our Immunization
Experiment 698
26.5 Building a Better Mousetrap 700
26.6 Summary 704
Exercises 704
27 Modeling the Term Structure 705
27.1 Overview 705
27.2 An Initial Example 705
27.3 Description of the Data 710
27.4 The Treasury Yield Curve 713
27.5 Computing Par Yields from a Zero-Coupon Yield Curve 715
27.6 Summary 716
Exercises 717
28 Calculating Default-Adjusted Expected Bond Returns 719
28.1 Overview 719
28.2 Calculating the Expected Bond Return in a One-Period
Framework 721
28.3 Calculating the Expected Bond Return in a Multiperiod
Framework 722
28.4 A Numerical Example 726
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28.5 Experimenting with the Example 728
28.6 Computing the Bond Expected Return for an Actual
Bond 730
28.7 Semiannual Transition Matrices 734
28.8 Computing Bond Beta 737
28.9 Summary 739
Exercises 740
V Technical Considerations 743
29 Generating Random Numbers 745
29.1 Overview 745
29.2 Rand( ) and Rnd: The Excel and VBA Random-Number
Generators 746
29.3 Testing Random-Number Generators 749
29.4 Generating Normally Distributed Random Numbers 754
29.5 Summary 762
Exercises 762
30 Data Tables 765
30.1 Overview 765
30.2 An Example 765
30.3 Setting Up a Data Table 766
30.4 Building a Two-Dimensional Data Table 768
30.5 An Aesthetic Note: Hiding the Formula Cells 769
30.6 Excel Data Tables Are Arrays 770
Exercises 771
31 Matrices 775
31.1 Overview 775
31.2 Matrix Operations 776
31.3 Matrix Inverses 779
31.4 Solving Systems of Simultaneous Linear Equations 781
Exercises 782
32 The Gauss-Seidel Method 785
32.1 Overview 785
32.2 A Simple Example 785
32.3 A More Concise Solution 786
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32.4 Conclusion 787
Exercises 787
33 Excel Functions 789
33.1 Overview 789
33.2 Financial Functions 789
33.3 Dates and Date Functions 796
33.4 The Functions XIRR and XNPV 802
33.5 Statistical Functions 805
33.6 Doing Regressions with Excel 808
33.7 Conditional Functions 815
33.8 Large and Rank, Percentile, and Percentrank 816
33.9 Count, CountA, CountIF 817
33.10 Boolean Functions 819
33.11 Offset 821
34 Using Array Functions and Formulas 825
34.1 Overview 825
34.2 Some Built-in Array Functions 825
34.3 Homemade Array Functions 830
34.4 Array Formulas with Matrices 833
Exercises 838
35 Some Excel Hints 841
35.1 Overview 841
35.2 Fast Copy: Filling in Data Next to a Filled-in Column 841
35.3 Multiline Cells 843
35.4 Writing on Multiple Spreadsheets 845
35.5 Text Functions in Excel 847
35.6 Chart Titles That Update 847
35.7 Getformula: A Useful Way of Annotating Spreadsheets 850
35.8 Putting Greek Symbols in Cells 853
35.9 Superscripts and Subscripts 854
35.10 Named Cells 856
35.11 Hiding Cells 857
35.12 Formula Auditing 859
35.13 Formulating Millions as Thousands 861
xix Contents
VI Introduction to Visual Basic for Applications 865
36 User-Defi ned Functions with VBA 867
36.1 Overview 867
36.2 Using the VBA Editor to Build a User-Defi ned Function 867
36.3 Providing Help for the User-Defi ned Functions in the
Function Wizard 872
36.4 Fixing Mistakes in VBA 875
36.5 Conditional Execution: Using If Statements in VBA
Functions 877
36.6 The Select Case Statement 882
36.7 Using Excel Functions in VBA 884
36.8 Using User-Defi ned Functions in User-Defi ned
Functions 885
Exercises 888
Appendix: Cell Errors in Excel and VBA 892
37 Types and Loops 895
37.1 Overview 895
37.2 Using Types 895
37.3 Variables and Variable Types 897
37.4 Boolean and Comparison Operators 901
37.5 Loops 904
37.6 Summary 913
Exercises 913
38 Macros and User Interaction 919
38.1 Overview 919
38.2 Macro Subroutines 919
38.3 User Output and the MsgBox Function 926
38.4 User Input and the InputBox Function 930
38.5 Modules 932
38.6 Summary 935
Exercises 935
39 Arrays 941
39.1 Overview 941
39.2 Simple Arrays 941